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  <section id="module-sympy.geometry.point">
<span id="points"></span><h1>Points<a class="headerlink" href="#module-sympy.geometry.point" title="Permalink to this headline">¶</a></h1>
<dl class="py class">
<dt class="sig sig-object py" id="sympy.geometry.point.Point">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.geometry.point.</span></span><span class="sig-name descname"><span class="pre">Point</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L39-L855"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point" title="Permalink to this definition">¶</a></dt>
<dd><p>A point in a n-dimensional Euclidean space.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>coords</strong> : sequence of n-coordinate values. In the special</p>
<blockquote>
<div><p>case where n=2 or 3, a Point2D or Point3D will be created
as appropriate.</p>
</div></blockquote>
<p><strong>evaluate</strong> : if <span class="math notranslate nohighlight">\(True\)</span> (default), all floats are turn into</p>
<blockquote>
<div><p>exact types.</p>
</div></blockquote>
<p><strong>dim</strong> : number of coordinates the point should have.  If coordinates</p>
<blockquote>
<div><p>are unspecified, they are padded with zeros.</p>
</div></blockquote>
<p><strong>on_morph</strong> : indicates what should happen when the number of</p>
<blockquote>
<div><p>coordinates of a point need to be changed by adding or
removing zeros.  Possible values are <span class="math notranslate nohighlight">\('warn'\)</span>, <span class="math notranslate nohighlight">\('error'\)</span>, or
<span class="math notranslate nohighlight">\(ignore\)</span> (default).  No warning or error is given when <span class="math notranslate nohighlight">\(*args\)</span>
is empty and <span class="math notranslate nohighlight">\(dim\)</span> is given. An error is always raised when
trying to remove nonzero coordinates.</p>
</div></blockquote>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>TypeError</strong> : When instantiating with anything but a Point or sequence</p>
<p><strong>ValueError</strong> : when instantiating with a sequence with length &lt; 2 or</p>
<blockquote>
<div><p>when trying to reduce dimensions if keyword <span class="math notranslate nohighlight">\(on_morph='error'\)</span> is
set.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="go">Point3D(1, 2, 3)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">Point2D(1, 2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="go">Point2D(0, x)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">(</span><span class="n">dim</span><span class="o">=</span><span class="mi">4</span><span class="p">)</span>
<span class="go">Point(0, 0, 0, 0)</span>
</pre></div>
</div>
<p>Floats are automatically converted to Rational unless the
evaluate flag is False:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">)</span>
<span class="go">Point2D(1/2, 1/4)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="n">evaluate</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="go">Point2D(0.5, 0.25)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="lines.html#sympy.geometry.line.Segment" title="sympy.geometry.line.Segment"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Segment</span></code></a></dt><dd><p>Connects two Points</p>
</dd>
</dl>
</div>
<p class="rubric">Attributes</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 60%" />
<col style="width: 40%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p>length</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>origin: A <span class="math notranslate nohighlight">\(Point\)</span> representing the origin of the</p></td>
<td><p>appropriately-dimensioned space.</p></td>
</tr>
</tbody>
</table>
<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.affine_rank">
<em class="property"><span class="pre">static</span> </em><span class="sig-name descname"><span class="pre">affine_rank</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L311-L331"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.affine_rank" title="Permalink to this definition">¶</a></dt>
<dd><p>The affine rank of a set of points is the dimension
of the smallest affine space containing all the points.
For example, if the points lie on a line (and are not all
the same) their affine rank is 1.  If the points lie on a plane
but not a line, their affine rank is 2.  By convention, the empty
set has affine rank -1.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.ambient_dimension">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">ambient_dimension</span></span><a class="headerlink" href="#sympy.geometry.point.Point.ambient_dimension" title="Permalink to this definition">¶</a></dt>
<dd><p>Number of components this point has.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.are_coplanar">
<em class="property"><span class="pre">classmethod</span> </em><span class="sig-name descname"><span class="pre">are_coplanar</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">points</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L338-L382"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.are_coplanar" title="Permalink to this definition">¶</a></dt>
<dd><p>Return True if there exists a plane in which all the points
lie.  A trivial True value is returned if <span class="math notranslate nohighlight">\(len(points) &lt; 3\)</span> or
all Points are 2-dimensional.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>A set of points</strong></p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>boolean</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError</strong> : if less than 3 unique points are given</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p2</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">7</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p3</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p4</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="o">.</span><span class="n">are_coplanar</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p5</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="o">.</span><span class="n">are_coplanar</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p5</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.canberra_distance">
<span class="sig-name descname"><span class="pre">canberra_distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L803-L847"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.canberra_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>The Canberra Distance from self to point p.</p>
<p>Returns the weighted sum of horizontal and vertical distances to
point p.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>p</strong> : Point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>canberra_distance</strong> : The weighted sum of horizontal and vertical</p>
<p>distances to point p. The weight used is the sum of absolute values</p>
<p>of the coordinates.</p>
</dd>
<dt class="field-odd">Raises</dt>
<dd class="field-odd"><p><strong>ValueError when both vectors are zero.</strong></p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">canberra_distance</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">1</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">canberra_distance</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">2</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point.distance" title="sympy.geometry.point.Point.distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point.distance</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.distance">
<span class="sig-name descname"><span class="pre">distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L384-L434"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.distance" title="Permalink to this definition">¶</a></dt>
<dd><p>The Euclidean distance between self and another GeometricEntity.</p>
<dl class="field-list">
<dt class="field-odd">Returns</dt>
<dd class="field-odd"><p><strong>distance</strong> : number or symbolic expression.</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>TypeError</strong> : if other is not recognized as a GeometricEntity or is a</p>
<blockquote>
<div><p>GeometricEntity for which distance is not defined.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point</span><span class="p">,</span> <span class="n">Line</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">l</span> <span class="o">=</span> <span class="n">Line</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">distance</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">5</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">distance</span><span class="p">(</span><span class="n">l</span><span class="p">)</span>
<span class="go">sqrt(2)</span>
</pre></div>
</div>
<p>The computed distance may be symbolic, too:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p3</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p3</span><span class="o">.</span><span class="n">distance</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="go">sqrt(x**2 + y**2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="lines.html#sympy.geometry.line.Segment.length" title="sympy.geometry.line.Segment.length"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Segment.length</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point.taxicab_distance" title="sympy.geometry.point.Point.taxicab_distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point.taxicab_distance</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.dot">
<span class="sig-name descname"><span class="pre">dot</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L436-L440"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.dot" title="Permalink to this definition">¶</a></dt>
<dd><p>Return dot product of self with another Point.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.equals">
<span class="sig-name descname"><span class="pre">equals</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L442-L447"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.equals" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns whether the coordinates of self and other agree.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.evalf">
<span class="sig-name descname"><span class="pre">evalf</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prec</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">options</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L449-L478"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.evalf" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the coordinates of the point.</p>
<p>This method will, where possible, create and return a new Point
where the coordinates are evaluated as floating point numbers to
the precision indicated (default=15).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>prec</strong> : int</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>point</strong> : Point</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span><span class="p">,</span> <span class="n">Rational</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="n">Rational</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">Rational</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span>
<span class="go">Point2D(1/2, 3/2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">evalf</span><span class="p">()</span>
<span class="go">Point2D(0.5, 1.5)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.intersection">
<span class="sig-name descname"><span class="pre">intersection</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L480-L519"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.intersection" title="Permalink to this definition">¶</a></dt>
<dd><p>The intersection between this point and another GeometryEntity.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>other</strong> : GeometryEntity or sequence of coordinates</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>intersection</strong> : list of Points</p>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The return value will either be an empty list if there is no
intersection, otherwise it will contain this point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">p3</span><span class="p">)</span>
<span class="go">[Point2D(0, 0)]</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.is_collinear">
<span class="sig-name descname"><span class="pre">is_collinear</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L521-L557"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.is_collinear" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <span class="math notranslate nohighlight">\(True\)</span> if there exists a line
that contains <span class="math notranslate nohighlight">\(self\)</span> and <span class="math notranslate nohighlight">\(points\)</span>.  Returns <span class="math notranslate nohighlight">\(False\)</span> otherwise.
A trivially True value is returned if no points are given.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>args</strong> : sequence of Points</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>is_collinear</strong> : boolean</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">,</span> <span class="n">p5</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="o">.</span><span class="n">is_collinear</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="o">.</span><span class="n">is_collinear</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p5</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="lines.html#sympy.geometry.line.Line" title="sympy.geometry.line.Line"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Line</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.is_concyclic">
<span class="sig-name descname"><span class="pre">is_concyclic</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L559-L613"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.is_concyclic" title="Permalink to this definition">¶</a></dt>
<dd><p>Do <span class="math notranslate nohighlight">\(self\)</span> and the given sequence of points lie in a circle?</p>
<p>Returns True if the set of points are concyclic and
False otherwise. A trivial value of True is returned
if there are fewer than 2 other points.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>args</strong> : sequence of Points</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>is_concyclic</strong> : boolean</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span>
</pre></div>
</div>
<p>Define 4 points that are on the unit circle:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p4</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="p">(</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">is_concyclic</span><span class="p">()</span> <span class="o">==</span> <span class="n">p1</span><span class="o">.</span><span class="n">is_concyclic</span><span class="p">(</span><span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">)</span> <span class="o">==</span> <span class="kc">True</span>
<span class="go">True</span>
</pre></div>
</div>
<p>Define a point not on that circle:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
</pre></div>
</div>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">is_concyclic</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.is_nonzero">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">is_nonzero</span></span><a class="headerlink" href="#sympy.geometry.point.Point.is_nonzero" title="Permalink to this definition">¶</a></dt>
<dd><p>True if any coordinate is nonzero, False if every coordinate is zero,
and None if it cannot be determined.</p>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.is_scalar_multiple">
<span class="sig-name descname"><span class="pre">is_scalar_multiple</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L624-L641"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.is_scalar_multiple" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns whether each coordinate of <span class="math notranslate nohighlight">\(self\)</span> is a scalar
multiple of the corresponding coordinate in point p.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.is_zero">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">is_zero</span></span><a class="headerlink" href="#sympy.geometry.point.Point.is_zero" title="Permalink to this definition">¶</a></dt>
<dd><p>True if every coordinate is zero, False if any coordinate is not zero,
and None if it cannot be determined.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.length">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">length</span></span><a class="headerlink" href="#sympy.geometry.point.Point.length" title="Permalink to this definition">¶</a></dt>
<dd><p>Treating a Point as a Line, this returns 0 for the length of a Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">length</span>
<span class="go">0</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.midpoint">
<span class="sig-name descname"><span class="pre">midpoint</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L669-L697"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.midpoint" title="Permalink to this definition">¶</a></dt>
<dd><p>The midpoint between self and point p.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>p</strong> : Point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>midpoint</strong> : Point</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">13</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">midpoint</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">Point2D(7, 3)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="lines.html#sympy.geometry.line.Segment.midpoint" title="sympy.geometry.line.Segment.midpoint"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Segment.midpoint</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.n">
<span class="sig-name descname"><span class="pre">n</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">prec</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">options</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L449-L478"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.n" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the coordinates of the point.</p>
<p>This method will, where possible, create and return a new Point
where the coordinates are evaluated as floating point numbers to
the precision indicated (default=15).</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>prec</strong> : int</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>point</strong> : Point</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point</span><span class="p">,</span> <span class="n">Rational</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="n">Rational</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">Rational</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span>
<span class="go">Point2D(1/2, 3/2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">evalf</span><span class="p">()</span>
<span class="go">Point2D(0.5, 1.5)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.origin">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">origin</span></span><a class="headerlink" href="#sympy.geometry.point.Point.origin" title="Permalink to this definition">¶</a></dt>
<dd><p>A point of all zeros of the same ambient dimension
as the current point</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.orthogonal_direction">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">orthogonal_direction</span></span><a class="headerlink" href="#sympy.geometry.point.Point.orthogonal_direction" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a non-zero point that is orthogonal to the
line containing <span class="math notranslate nohighlight">\(self\)</span> and the origin.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Line</span><span class="p">,</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span><span class="o">.</span><span class="n">orthogonal_direction</span>
<span class="go">Point3D(-2, 1, 0)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">_</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Line</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">b</span><span class="o">.</span><span class="n">origin</span><span class="p">)</span><span class="o">.</span><span class="n">is_perpendicular</span><span class="p">(</span><span class="n">Line</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">origin</span><span class="p">))</span>
<span class="go">True</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.project">
<em class="property"><span class="pre">static</span> </em><span class="sig-name descname"><span class="pre">project</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">a</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L731-L768"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.project" title="Permalink to this definition">¶</a></dt>
<dd><p>Project the point <span class="math notranslate nohighlight">\(a\)</span> onto the line between the origin
and point <span class="math notranslate nohighlight">\(b\)</span> along the normal direction.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>a</strong> : Point</p>
<p><strong>b</strong> : Point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>p</strong> : Point</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Line</span><span class="p">,</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">a</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">b</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">z</span> <span class="o">=</span> <span class="n">a</span><span class="o">.</span><span class="n">origin</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point</span><span class="o">.</span><span class="n">project</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Line</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span><span class="o">.</span><span class="n">is_perpendicular</span><span class="p">(</span><span class="n">Line</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">b</span><span class="p">))</span>
<span class="go">True</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point</span><span class="o">.</span><span class="n">is_collinear</span><span class="p">(</span><span class="n">z</span><span class="p">,</span> <span class="n">p</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
<span class="go">True</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="lines.html#sympy.geometry.line.LinearEntity.projection" title="sympy.geometry.line.LinearEntity.projection"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.LinearEntity.projection</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.taxicab_distance">
<span class="sig-name descname"><span class="pre">taxicab_distance</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L770-L801"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point.taxicab_distance" title="Permalink to this definition">¶</a></dt>
<dd><p>The Taxicab Distance from self to point p.</p>
<p>Returns the sum of the horizontal and vertical distances to point p.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>p</strong> : Point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>taxicab_distance</strong> : The sum of the horizontal</p>
<p>and vertical distances to point p.</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point</span><span class="p">(</span><span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">taxicab_distance</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">7</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point.distance" title="sympy.geometry.point.Point.distance"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point.distance</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point.unit">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">unit</span></span><a class="headerlink" href="#sympy.geometry.point.Point.unit" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the Point that is in the same direction as <span class="math notranslate nohighlight">\(self\)</span>
and a distance of 1 from the origin</p>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.geometry.point.</span></span><span class="sig-name descname"><span class="pre">Point2D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">_nocheck</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L857-L1069"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point2D" title="Permalink to this definition">¶</a></dt>
<dd><p>A point in a 2-dimensional Euclidean space.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>coords</strong> : sequence of 2 coordinate values.</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>TypeError</strong></p>
<blockquote>
<div><p>When trying to add or subtract points with different dimensions.
When trying to create a point with more than two dimensions.
When <span class="math notranslate nohighlight">\(intersection\)</span> is called with object other than a Point.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.geometry</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point2D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(1, 2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point2D</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">])</span>
<span class="go">Point2D(1, 2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point2D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
<span class="go">Point2D(0, x)</span>
</pre></div>
</div>
<p>Floats are automatically converted to Rational unless the
evaluate flag is False:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Point2D</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">)</span>
<span class="go">Point2D(1/2, 1/4)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point2D</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="n">evaluate</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="go">Point2D(0.5, 0.25)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<dl class="simple">
<dt><a class="reference internal" href="lines.html#sympy.geometry.line.Segment" title="sympy.geometry.line.Segment"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Segment</span></code></a></dt><dd><p>Connects two Points</p>
</dd>
</dl>
</div>
<p class="rubric">Attributes</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 38%" />
<col style="width: 63%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p>x</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>y</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>length</p></td>
<td></td>
</tr>
</tbody>
</table>
<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.bounds">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">bounds</span></span><a class="headerlink" href="#sympy.geometry.point.Point2D.bounds" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a tuple (xmin, ymin, xmax, ymax) representing the bounding
rectangle for the geometric figure.</p>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.coordinates">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">coordinates</span></span><a class="headerlink" href="#sympy.geometry.point.Point2D.coordinates" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the two coordinates of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">coordinates</span>
<span class="go">(0, 1)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.rotate">
<span class="sig-name descname"><span class="pre">rotate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">angle</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L927-L959"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point2D.rotate" title="Permalink to this definition">¶</a></dt>
<dd><p>Rotate <code class="docutils literal notranslate"><span class="pre">angle</span></code> radians counterclockwise about Point <code class="docutils literal notranslate"><span class="pre">pt</span></code>.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span><span class="p">,</span> <span class="n">pi</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(0, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">rotate</span><span class="p">(</span><span class="n">pi</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
<span class="go">Point2D(2, -1)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point2D.translate" title="sympy.geometry.point.Point2D.translate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">translate</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point2D.scale" title="sympy.geometry.point.Point2D.scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scale</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.scale">
<span class="sig-name descname"><span class="pre">scale</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L961-L986"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point2D.scale" title="Permalink to this definition">¶</a></dt>
<dd><p>Scale the coordinates of the Point by multiplying by
<code class="docutils literal notranslate"><span class="pre">x</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code> after subtracting <code class="docutils literal notranslate"><span class="pre">pt</span></code> – default is (0, 0) –
and then adding <code class="docutils literal notranslate"><span class="pre">pt</span></code> back again (i.e. <code class="docutils literal notranslate"><span class="pre">pt</span></code> is the point of
reference for the scaling).</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(2, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(2, 2)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point2D.rotate" title="sympy.geometry.point.Point2D.rotate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">rotate</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point2D.translate" title="sympy.geometry.point.Point2D.translate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">translate</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.transform">
<span class="sig-name descname"><span class="pre">transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">matrix</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L988-L1001"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point2D.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the point after applying the transformation described
by the 3x3 Matrix, <code class="docutils literal notranslate"><span class="pre">matrix</span></code>.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point2D.rotate" title="sympy.geometry.point.Point2D.rotate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point2D.rotate</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point2D.scale" title="sympy.geometry.point.Point2D.scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point2D.scale</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point2D.translate" title="sympy.geometry.point.Point2D.translate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point2D.translate</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.translate">
<span class="sig-name descname"><span class="pre">translate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1003-L1024"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point2D.translate" title="Permalink to this definition">¶</a></dt>
<dd><p>Shift the Point by adding x and y to the coordinates of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(2, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(2, 3)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">+</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point2D(2, 3)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point2D.rotate" title="sympy.geometry.point.Point2D.rotate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point2D.rotate</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point2D.scale" title="sympy.geometry.point.Point2D.scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scale</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.x">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">x</span></span><a class="headerlink" href="#sympy.geometry.point.Point2D.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the X coordinate of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">x</span>
<span class="go">0</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point2D.y">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">y</span></span><a class="headerlink" href="#sympy.geometry.point.Point2D.y" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the Y coordinate of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point2D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point2D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">y</span>
<span class="go">1</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

<dl class="py class">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D">
<em class="property"><span class="pre">class</span> </em><span class="sig-prename descclassname"><span class="pre">sympy.geometry.point.</span></span><span class="sig-name descname"><span class="pre">Point3D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">args</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">_nocheck</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">False</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">kwargs</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1071-L1376"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D" title="Permalink to this definition">¶</a></dt>
<dd><p>A point in a 3-dimensional Euclidean space.</p>
<dl class="field-list">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>coords</strong> : sequence of 3 coordinate values.</p>
</dd>
<dt class="field-even">Raises</dt>
<dd class="field-even"><p><strong>TypeError</strong></p>
<blockquote>
<div><p>When trying to add or subtract points with different dimensions.
When <span class="math notranslate nohighlight">\(intersection\)</span> is called with object other than a Point.</p>
</div></blockquote>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="go">Point3D(1, 2, 3)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="p">([</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">])</span>
<span class="go">Point3D(1, 2, 3)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="go">Point3D(0, x, 3)</span>
</pre></div>
</div>
<p>Floats are automatically converted to Rational unless the
evaluate flag is False:</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(1/2, 1/4, 2)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">evaluate</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
<span class="go">Point3D(0.5, 0.25, 3)</span>
</pre></div>
</div>
<p class="rubric">Attributes</p>
<table class="docutils align-default">
<colgroup>
<col style="width: 38%" />
<col style="width: 63%" />
</colgroup>
<tbody>
<tr class="row-odd"><td><p>x</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>y</p></td>
<td></td>
</tr>
<tr class="row-odd"><td><p>z</p></td>
<td></td>
</tr>
<tr class="row-even"><td><p>length</p></td>
<td></td>
</tr>
</tbody>
</table>
<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.are_collinear">
<em class="property"><span class="pre">static</span> </em><span class="sig-name descname"><span class="pre">are_collinear</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="o"><span class="pre">*</span></span><span class="n"><span class="pre">points</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1127-L1161"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.are_collinear" title="Permalink to this definition">¶</a></dt>
<dd><p>Is a sequence of points collinear?</p>
<p>Test whether or not a set of points are collinear. Returns True if
the set of points are collinear, or False otherwise.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>points</strong> : sequence of Point</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>are_collinear</strong> : boolean</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy.abc</span> <span class="kn">import</span> <span class="n">x</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">,</span> <span class="n">p5</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="n">Point3D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">),</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">6</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="o">.</span><span class="n">are_collinear</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p4</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">Point3D</span><span class="o">.</span><span class="n">are_collinear</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">p5</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="lines.html#sympy.geometry.line.Line3D" title="sympy.geometry.line.Line3D"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.line.Line3D</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.coordinates">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">coordinates</span></span><a class="headerlink" href="#sympy.geometry.point.Point3D.coordinates" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the three coordinates of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">coordinates</span>
<span class="go">(0, 1, 2)</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.direction_cosine">
<span class="sig-name descname"><span class="pre">direction_cosine</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">point</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1163-L1188"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.direction_cosine" title="Permalink to this definition">¶</a></dt>
<dd><p>Gives the direction cosine between 2 points</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>p</strong> : Point3D</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>list</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">direction_cosine</span><span class="p">(</span><span class="n">Point3D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="go">[sqrt(6)/6, sqrt(6)/6, sqrt(6)/3]</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.direction_ratio">
<span class="sig-name descname"><span class="pre">direction_ratio</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">point</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1190-L1212"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.direction_ratio" title="Permalink to this definition">¶</a></dt>
<dd><p>Gives the direction ratio between 2 points</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>p</strong> : Point3D</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p>list</p>
</dd>
</dl>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">direction_ratio</span><span class="p">(</span><span class="n">Point3D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">5</span><span class="p">))</span>
<span class="go">[1, 1, 2]</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.intersection">
<span class="sig-name descname"><span class="pre">intersection</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">other</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1214-L1250"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.intersection" title="Permalink to this definition">¶</a></dt>
<dd><p>The intersection between this point and another GeometryEntity.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters</dt>
<dd class="field-odd"><p><strong>other</strong> : GeometryEntity or sequence of coordinates</p>
</dd>
<dt class="field-even">Returns</dt>
<dd class="field-even"><p><strong>intersection</strong> : list of Points</p>
</dd>
</dl>
<p class="rubric">Notes</p>
<p>The return value will either be an empty list if there is no
intersection, otherwise it will contain this point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">p2</span><span class="p">)</span>
<span class="go">[]</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p1</span><span class="o">.</span><span class="n">intersection</span><span class="p">(</span><span class="n">p3</span><span class="p">)</span>
<span class="go">[Point3D(0, 0, 0)]</span>
</pre></div>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.scale">
<span class="sig-name descname"><span class="pre">scale</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">pt</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1252-L1277"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.scale" title="Permalink to this definition">¶</a></dt>
<dd><p>Scale the coordinates of the Point by multiplying by
<code class="docutils literal notranslate"><span class="pre">x</span></code> and <code class="docutils literal notranslate"><span class="pre">y</span></code> after subtracting <code class="docutils literal notranslate"><span class="pre">pt</span></code> – default is (0, 0) –
and then adding <code class="docutils literal notranslate"><span class="pre">pt</span></code> back again (i.e. <code class="docutils literal notranslate"><span class="pre">pt</span></code> is the point of
reference for the scaling).</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(2, 1, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">scale</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(2, 2, 1)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point3D.translate" title="sympy.geometry.point.Point3D.translate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">translate</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.transform">
<span class="sig-name descname"><span class="pre">transform</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">matrix</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1279-L1293"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.transform" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the point after applying the transformation described
by the 4x4 Matrix, <code class="docutils literal notranslate"><span class="pre">matrix</span></code>.</p>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point3D.scale" title="sympy.geometry.point.Point3D.scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point3D.scale</span></code></a>, <a class="reference internal" href="#sympy.geometry.point.Point3D.translate" title="sympy.geometry.point.Point3D.translate"><code class="xref py py-obj docutils literal notranslate"><span class="pre">sympy.geometry.point.Point3D.translate</span></code></a></p>
</div>
</dd></dl>

<dl class="py method">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.translate">
<span class="sig-name descname"><span class="pre">translate</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">z</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0</span></span></em><span class="sig-paren">)</span><a class="reference external" href="https://github.com/sympy/sympy/blob/00d6469eafdd4aac346a0b598184c15f2560dbe5/sympy/geometry/point.py#L1295-L1316"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#sympy.geometry.point.Point3D.translate" title="Permalink to this definition">¶</a></dt>
<dd><p>Shift the Point by adding x and y to the coordinates of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(2, 1, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span><span class="o">.</span><span class="n">translate</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(2, 3, 1)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">t</span> <span class="o">+</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Point3D(2, 3, 3)</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="admonition-title">See also</p>
<p><a class="reference internal" href="#sympy.geometry.point.Point3D.scale" title="sympy.geometry.point.Point3D.scale"><code class="xref py py-obj docutils literal notranslate"><span class="pre">scale</span></code></a></p>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.x">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">x</span></span><a class="headerlink" href="#sympy.geometry.point.Point3D.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the X coordinate of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">3</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">x</span>
<span class="go">0</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.y">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">y</span></span><a class="headerlink" href="#sympy.geometry.point.Point3D.y" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the Y coordinate of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">y</span>
<span class="go">1</span>
</pre></div>
</div>
</dd></dl>

<dl class="py property">
<dt class="sig sig-object py" id="sympy.geometry.point.Point3D.z">
<em class="property"><span class="pre">property</span> </em><span class="sig-name descname"><span class="pre">z</span></span><a class="headerlink" href="#sympy.geometry.point.Point3D.z" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the Z coordinate of the Point.</p>
<p class="rubric">Examples</p>
<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">&gt;&gt;&gt; </span><span class="kn">from</span> <span class="nn">sympy</span> <span class="kn">import</span> <span class="n">Point3D</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span> <span class="o">=</span> <span class="n">Point3D</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="gp">&gt;&gt;&gt; </span><span class="n">p</span><span class="o">.</span><span class="n">z</span>
<span class="go">1</span>
</pre></div>
</div>
</dd></dl>

</dd></dl>

</section>


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